When you set up a Gift Certificate product, your shopper has the ability to purchase the gift certificate and send it to someone of their choosing. That recipient will then receive an email with the gift certificate code they'll be able to use on your store.
Unfortunately, if that email is lost or otherwise not received by the recipient, there is no way of resending it to them.
However, as merchant you are able to retrieve it by looking at the order that generated the Gift Certificate itself.
Log into your Shift4Shop Online Store Manager.
Using the left navigation menu, go to Orders > Manage Orders.
Locate the order that was placed for the gift certificate and open it.
While viewing the order, scroll down to the bottom and expand the section labeled "Gift Certificates Purchased" to see the issued gift certificate code. You may then provide the code to your customer so they can provide it to their recipient.